Publications

Recent PublicationsEditorial WorkExtended AbstractsOut SoonVoluntary Work

Recent Publications

  1. SMT-Solving Combinatorial Inequalities, with James H. Davenport and Matthew England (accepted, 7th SC^2 Workshop, Federated Logic Conference 2022 Proceedings )
  2. ArXiv On Finite Analogs of Schmidt’s Problem and Its Variants, with Alexander Berkovich (submitted)
  3. ArXiv Weighted Cylindric Partitions, with Walter Bridges (submitted)
  4. ArXiv Sequences in Overpartitions, with George E. Andrews (submitted)
  5. Practical Evaluation of Quantifier Elimination Methods, with James H. Davenport, and Zak P. Tonks. (accepted, 6th SC^2 Workshop Proceedings, SIAM Conference on Applied Algebraic Geometry Conference 2021 Proceedings)
  6. ArXiv New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, with Alexander Berkovich. J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125678, 18 pp.
  7. ArXiv Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities, with Wadim Zudilin. Séminaire Lotharingien de Combinatoire, B85e (2021), 17 pp
  8. ArXiv Cylindric Partitions and some new A_2 Rogers-Ramanujan Identities, with Sylvie Corteel and Jehanne Dousse. (accepted, Proc. Amer. Math. Soc.) https://doi.org/10.1090/proc/15570
  9. ArXiv qFunctions – A Mathematica package for q-series and partition theory applications, with Jakob Ablinger. Journal of Symbolic Computation 107 (2021), 145-166.
  10. ArXiv Logconcavity results for a biparametric and an elliptic extension of the q-binomial coefficients, with Michael Schlosser and  Koushik Senapati. Int. J. Number Theory 17 (2021), no. 3, 787–804.
  11. ArXiv Where do the maximum absolute q-series coefficients of (1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n) occur?, with Alexander Berkovich. Experimental Mathematics, DOI: 10.1080/10586458.2020.1776177
  12. ArXiv On a weighted spin of the Lebesgue Identity. Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science, vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_20
  13. ArXiv A Polynomial Identity Implying Schur’s Partition Theorem. Proc. Amer. Math. Soc. 148 (2020), 3307-3324
  14. ArXiv On Double Sum Generating Functions in Connection with Some Classical Partition Theorems. Disc. Math J. Volume 344, Issue 11, (2021), 112562
  15. ArXiv Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, with Alexander Berkovich. Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_4
  16. ArXiv Elementary Polynomial Identities Involving q-Trinomial Coefficients, with Alexander Berkovich. Ann. Comb. 23 (2019), 549–560.
  17. ArXiv Polynomial Identities Implying Capparelli’s Partition Theorems, with Alexander Berkovich. J. Number Theory 201 (2019), 77-107.
  18. ArXiv Some Elementary Partition Inequalities and Their Implications, with Alexander Berkovich. Ann. Comb. 23 (2019), 263-284.
  19. ArXiv Weighted Rogers-Ramanujan Partitions and Dyson Crank.  Ramanujan J. 46 (2018), no. 2, 579–591.
  20. ArXiv On Some Polynomials and Series of Bloch-Polya Type, with Alexander Berkovich. Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827–2838.
  21. ArXiv New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions, with Alexander Berkovich. ALLADI 60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series (2017) pp 69-94 Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)
  22. ArXiv Variation on a theme of Nathan Fine. New weighted partition identities, with Alexander Berkovich. J. Number Theory 176 (2017), 226–248.
  23. ArXiv On partitions with fixed number of even-indexed and odd-indexed odd parts, with Alexander Berkovich. J. Number Theory 167 (2016), 7–30.
  24. ArXiv A New Companion to Capparelli’s Identities, with Alexander Berkovich. Adv. in Appl. Math. 71 (2015), 125–137.

Editorial Work

  1. Guest Editor: Mathematics in Computer Science – ACA 2021 (Virtual Online) Special Issue, with Ilias Kotsireas and Dimitris Simos, published by Birkhauser Springer.

Extended Abstracts

  1. qFunctions: A Mathematica package for partition theory applications, and its future, Computer Algebra in Scientific Computing 2021 (CASC 21) Proceedings.
  2. ArXiv The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, with Russell Bradford, James H. Davenport, Matthew England, and Amirhossein Sadeghimanesh. ISSAC 2021 https://dl.acm.org/doi/abs/10.1145/3511528.3511538
  3. On q-Rising Factorials and the Necessity of Shared Memory Calculations. Austrian High-Performance-Computing meeting (AHPC2020), Publisher: Institute of Science and Technology Austria, Klosterneuburg Austria, Editors: Alois Schlögl et al. ISBN: 978-3-99078-004-6

Soon to be Public

  • On more conjectural identities modulo 16 and 20, joint with George E. Andrews
  • Counting  on 4-decorated diagrams.

Voluntary Work

A list of journals I wrote reports for can be found here.

Reviewer for American Mathematical Society MathSciNet.

Judge at MAA Committee on Undergraduate poster session at JMM 2019 and 2020.

Judge at CMS Summer Meeting 2021 Undergraduate poster session.